Block #371,413

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/22/2014, 8:21:21 PM · Difficulty 10.4359 · 6,455,794 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c32bfb8efbe76da4c233caa8accc5d6dbc9f64e0c3a9f7a0602d1b4a8b8b4ad

View on Chainz ↗

Height

#371,413

Difficulty

10.435939

Transactions

Size

1.09 KB

Version

Bits

0a6f99b9

Nonce

17,280

Timestamp

1/22/2014, 8:21:21 PM

Confirmations

6,455,794

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

91a275e61fbb356b58a5ecd4925f85a9987cc7aa6681eb771986f1277d37b989

Transactions (5)

Coinbasea8aebb3dc02ee7…d4d39223191d85

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

607134c5790a40…8a71fcde62cb04

1 in → 2 out9.1500 XPM227 B

AKZ3vx2y…939mdRLq AMYe9LRv…jRD62tJF

87f8ac67467134…8e081010ad1d7c

1 in → 2 out8.1310 XPM226 B

Aay1SRBo…eBLzetH7 ANMKXeZC…DkHaKZBG

60c7432c7a9602…268beba8444366

1 in → 2 out8.0794 XPM227 B

ASQgSF79…95Y9PzPf AK2Tz82K…qe5K9gwM

3be0e0a82fa88d…adfe01e2ae78c7

1 in → 2 out6.0910 XPM227 B

AHUwqKXL…1KFrLZLC AR7n9chB…ozyWpotN

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.

3.227 × 10⁹⁸(99-digit number)

32279994483556357072…74223729804024155519

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

3.227 × 10⁹⁸(99-digit number)

32279994483556357072…74223729804024155519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.227 × 10⁹⁸(99-digit number)

32279994483556357072…74223729804024155521

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

6.455 × 10⁹⁸(99-digit number)

64559988967112714144…48447459608048311039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.455 × 10⁹⁸(99-digit number)

64559988967112714144…48447459608048311041

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

1.291 × 10⁹⁹(100-digit number)

12911997793422542828…96894919216096622079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.291 × 10⁹⁹(100-digit number)

12911997793422542828…96894919216096622081

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

2.582 × 10⁹⁹(100-digit number)

25823995586845085657…93789838432193244159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.582 × 10⁹⁹(100-digit number)

25823995586845085657…93789838432193244161

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

5.164 × 10⁹⁹(100-digit number)

51647991173690171315…87579676864386488319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.164 × 10⁹⁹(100-digit number)

51647991173690171315…87579676864386488321

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 #371,413

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