Block #602,632

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/26/2014, 10:35:55 AM · Difficulty 10.9132 · 6,223,669 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82efe18ac1e47e6b384ddcce3ddec905b6e25b7ff77f99a5d46b16b923946971

View on Chainz ↗

Height

#602,632

Difficulty

10.913158

Transactions

Size

884 B

Version

Bits

0ae9c4ba

Nonce

379,028,685

Timestamp

6/26/2014, 10:35:55 AM

Confirmations

6,223,669

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c83e85e50ac073b2fbbe3a141f4a69e07271d5b6b7aca1777e0e9e3c4918ddb5

Transactions (4)

Coinbaseed23172746297f…eaeb6194917544

1 in → 1 out8.4100 XPM116 B

ANSXnLY2…Sd25TjkD

31cfa2f65a94a4…d12fdc12e9ab5d

1 in → 2 out8.3400 XPM225 B

AW6ei9Gv…9VigGijR Abi8nFbt…bkDhGPuE

ab7c658e64ab34…544150fd0b6fdf

1 in → 2 out7.7766 XPM225 B

ATUJFkEF…j71DTZhm AUnpsFY3…iqmPJbV6

cf20bdf26fc6d8…983f74c69f8bf8

1 in → 2 out7.7706 XPM225 B

AMVLqtrh…STPzUAA3 AZS4yuXr…deWqZ51K

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.

3.151 × 10¹⁰¹(102-digit number)

31517625098368327849…59593794484840366079

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

3.151 × 10¹⁰¹(102-digit number)

31517625098368327849…59593794484840366079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.151 × 10¹⁰¹(102-digit number)

31517625098368327849…59593794484840366081

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

6.303 × 10¹⁰¹(102-digit number)

63035250196736655698…19187588969680732159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.303 × 10¹⁰¹(102-digit number)

63035250196736655698…19187588969680732161

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

1.260 × 10¹⁰²(103-digit number)

12607050039347331139…38375177939361464319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.260 × 10¹⁰²(103-digit number)

12607050039347331139…38375177939361464321

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

2.521 × 10¹⁰²(103-digit number)

25214100078694662279…76750355878722928639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.521 × 10¹⁰²(103-digit number)

25214100078694662279…76750355878722928641

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

5.042 × 10¹⁰²(103-digit number)

50428200157389324558…53500711757445857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.042 × 10¹⁰²(103-digit number)

50428200157389324558…53500711757445857281

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 #602,632

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