Block #1,372,758

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2015, 11:09:24 AM · Difficulty 10.8083 · 5,432,045 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b8724d0bb7b1a5382ef6c463f2c072fb0e73ac94739b4f695d992f0659a101fd

View on Chainz ↗

Height

#1,372,758

Difficulty

10.808341

Transactions

Size

970 B

Version

Bits

0aceef68

Nonce

1,255,787,328

Timestamp

12/17/2015, 11:09:24 AM

Confirmations

5,432,045

Mined by

⛏️ P2SHAVqPjzgftDpGAEhhKK24UmxWQ9rxdj8e3f

Merkle Root

d6a2168b853ed3a76c5810ff02b53a267317db88e43ac3d8e9c490d7fd3b669f

Transactions (2)

Coinbase4dba253677fef3…3370b866f62c69

1 in → 1 out8.5600 XPM109 B

AVqPjzgf…rxdj8e3f

e5961b2e6577fa…9155523bb897b6

1 in → 18 out1.4370 XPM770 B

ASf56EmJ…urQdVeD5 AYByaohL…yE2waq3Z AJaEADqq…YxQdFCjN AeWwtQn7…mkHp8D2j AZdido3s…umKEg2dZ

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.

1.748 × 10⁹⁶(97-digit number)

17482752222641386910…39796914100973337599

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

1.748 × 10⁹⁶(97-digit number)

17482752222641386910…39796914100973337599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.748 × 10⁹⁶(97-digit number)

17482752222641386910…39796914100973337601

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

3.496 × 10⁹⁶(97-digit number)

34965504445282773821…79593828201946675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.496 × 10⁹⁶(97-digit number)

34965504445282773821…79593828201946675201

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

6.993 × 10⁹⁶(97-digit number)

69931008890565547642…59187656403893350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.993 × 10⁹⁶(97-digit number)

69931008890565547642…59187656403893350401

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

1.398 × 10⁹⁷(98-digit number)

13986201778113109528…18375312807786700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.398 × 10⁹⁷(98-digit number)

13986201778113109528…18375312807786700801

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

2.797 × 10⁹⁷(98-digit number)

27972403556226219056…36750625615573401599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.797 × 10⁹⁷(98-digit number)

27972403556226219056…36750625615573401601

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