Block #377,662

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 7:18:58 AM · Difficulty 10.4184 · 6,429,789 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc3ec57e60c1afc312d7f02c005206e072557f852e2f0b47be1c40a9e2611e88

View on Chainz ↗

Height

#377,662

Difficulty

10.418388

Transactions

Size

1.28 KB

Version

Bits

0a6b1b74

Nonce

282,366

Timestamp

1/27/2014, 7:18:58 AM

Confirmations

6,429,789

Mined by

⛏️ P2SHAb64gm8KUnFNR9oWChHpwHnuPjmwRnN1CH

Merkle Root

0f27f31bd5512b75de125bc0b7a6443b2aebd1105626252f9f4caf5bdff8dcab

Transactions (4)

Coinbasec0f6776d1b45ad…5e151c5ca5a4c2

1 in → 1 out9.2300 XPM109 B

Ab64gm8K…mwRnN1CH

f5732a4bf8ef5e…7dea5d62fe4d03

3 in → 10 out27.8400 XPM692 B

AHFBQZvJ…RuyPvMzo AeXJa6Wa…nc2thavR ANqJPxk9…rKume2u6 AKtwSk6i…vifEVgVe AKpWfTgS…JDmAtbgJ

d09bda5312a5a1…2e9afc65db25eb

1 in → 2 out82.1625 XPM227 B

AaN8Bgrs…JFqwkhsD AdK1pg3i…4LRDuwBA

fd25df8dfaec6c…cdcba5136fc496

1 in → 1 out6.7833 XPM193 B

AYukZDLG…L1spRFjP

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.

4.503 × 10⁹⁵(96-digit number)

45033781345776766702…79774450824545028379

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

4.503 × 10⁹⁵(96-digit number)

45033781345776766702…79774450824545028379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.503 × 10⁹⁵(96-digit number)

45033781345776766702…79774450824545028381

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

9.006 × 10⁹⁵(96-digit number)

90067562691553533405…59548901649090056759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.006 × 10⁹⁵(96-digit number)

90067562691553533405…59548901649090056761

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

1.801 × 10⁹⁶(97-digit number)

18013512538310706681…19097803298180113519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.801 × 10⁹⁶(97-digit number)

18013512538310706681…19097803298180113521

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

3.602 × 10⁹⁶(97-digit number)

36027025076621413362…38195606596360227039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.602 × 10⁹⁶(97-digit number)

36027025076621413362…38195606596360227041

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

7.205 × 10⁹⁶(97-digit number)

72054050153242826724…76391213192720454079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.205 × 10⁹⁶(97-digit number)

72054050153242826724…76391213192720454081

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 #377,662

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