Block #1,596,697

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2016, 1:27:07 PM · Difficulty 10.6120 · 5,212,536 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

ead67da8ed07a10c452668600c8c08934398edd660ecb3cd1e467041bd14481d

View on Chainz ↗

Height

#1,596,697

Difficulty

10.612040

Transactions

Size

8.02 KB

Version

Bits

0a9caeae

Nonce

1,607,841,710

Timestamp

5/23/2016, 1:27:07 PM

Confirmations

5,212,536

Mined by

⛏️ P2SHAHumpc8Lj1q4DaMyk52pz8stWT8Cpeb4wH

Merkle Root

572eaae09f52903ca0cf38cc94991f3dd36feadb0fefe46a57c5d5b2c72a2b41

Transactions (5)

Coinbase21d9081a668f6a…62cc7f201248a3

1 in → 1 out8.9600 XPM109 B

AHumpc8L…8Cpeb4wH

3f11a1b6513f6d…a7c65b1c9e517c

1 in → 51 out23.8592 XPM1.85 KB

AaPqwLUq…gVp9JdPo AZ3cZHxS…1qdoLqba AYCekZk5…3ZGrTA7D AcJmW6UY…SbrKT6UG AHBoK4dh…m8D5UwTc

97c82a158b42bf…6b8855f5535e97

4 in → 51 out5.4055 XPM2.28 KB

ANNMAvtF…mEXi7Pgg ARGaeBUX…2KkeUCy1 AGxKtv7S…oK3GtSwn AabArXgx…aWijWvZb AXTxG1Ry…bYA4mE3a

2675bff5b973a8…837b16559a2e51

1 in → 51 out3.5606 XPM1.85 KB

AKobQr5q…EdKZTdDu AcFcRirZ…8DFZboio ASWrAqET…TdVD9rjD AGgctm4J…U9boAuQz AaQh1sFD…nQDvuTYJ

97f1157ff23056…5cdbe358b9f55c

1 in → 51 out2.8800 XPM1.85 KB

ALd1iCgz…4gCc51ar AXEsAfGW…LPb7LnbB APq3W9Lb…crMXdVYw AGj6kiy2…MJXDUtnH AdBJdoHv…wgQKuCmu

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.338 × 10⁹⁶(97-digit number)

43384755783803284366…65285991314725242879

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

4.338 × 10⁹⁶(97-digit number)

43384755783803284366…65285991314725242879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.338 × 10⁹⁶(97-digit number)

43384755783803284366…65285991314725242881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

8.676 × 10⁹⁶(97-digit number)

86769511567606568733…30571982629450485759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.676 × 10⁹⁶(97-digit number)

86769511567606568733…30571982629450485761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.735 × 10⁹⁷(98-digit number)

17353902313521313746…61143965258900971519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.735 × 10⁹⁷(98-digit number)

17353902313521313746…61143965258900971521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.470 × 10⁹⁷(98-digit number)

34707804627042627493…22287930517801943039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.470 × 10⁹⁷(98-digit number)

34707804627042627493…22287930517801943041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

6.941 × 10⁹⁷(98-digit number)

69415609254085254986…44575861035603886079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.941 × 10⁹⁷(98-digit number)

69415609254085254986…44575861035603886081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,596,697

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