Block #837,855

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2014, 5:12:20 AM · Difficulty 10.9753 · 6,007,476 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59a20c17d588ee86b29123f753c55c42ad0db294d5e1c26915d2e864261b8029

View on Chainz ↗

Height

#837,855

Difficulty

10.975289

Transactions

Size

659 B

Version

Bits

0af9ac8e

Nonce

340,885,024

Timestamp

12/3/2014, 5:12:20 AM

Confirmations

6,007,476

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dff6723e1b3682eed25424b0e74d8a19577b2adb697c4115ab459492c09e4d69

Transactions (3)

Coinbase7c7fa81e8576b1…521b17cf42da81

1 in → 1 out8.3150 XPM116 B

ANSXnLY2…Sd25TjkD

bf111119ca219e…daeb617a7e3410

1 in → 2 out4.7109 XPM226 B

AWeFTqSF…usRDA3NM AUM5YuB2…W2JcaNA7

e3d9f60164a0fc…5a459f78248b77

1 in → 2 out0.4288 XPM226 B

AbBnqFAP…1iBiDCRy AGd1VPku…Ys641vTX

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.

7.213 × 10⁹⁶(97-digit number)

72131559541841305108…43188642140153561599

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

7.213 × 10⁹⁶(97-digit number)

72131559541841305108…43188642140153561599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.213 × 10⁹⁶(97-digit number)

72131559541841305108…43188642140153561601

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

1.442 × 10⁹⁷(98-digit number)

14426311908368261021…86377284280307123199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.442 × 10⁹⁷(98-digit number)

14426311908368261021…86377284280307123201

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

2.885 × 10⁹⁷(98-digit number)

28852623816736522043…72754568560614246399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.885 × 10⁹⁷(98-digit number)

28852623816736522043…72754568560614246401

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

5.770 × 10⁹⁷(98-digit number)

57705247633473044086…45509137121228492799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.770 × 10⁹⁷(98-digit number)

57705247633473044086…45509137121228492801

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

1.154 × 10⁹⁸(99-digit number)

11541049526694608817…91018274242456985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.154 × 10⁹⁸(99-digit number)

11541049526694608817…91018274242456985601

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 #837,855

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