Block #937,353

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/15/2015, 10:17:42 AM · Difficulty 10.9007 · 5,872,096 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cf784be32f93f20089938957188ea970a63ae7f012cbec3560c1e3984d7e084f

View on Chainz ↗

Height

#937,353

Difficulty

10.900699

Transactions

Size

591 B

Version

Bits

0ae6942e

Nonce

81,162,673

Timestamp

2/15/2015, 10:17:42 AM

Confirmations

5,872,096

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5394738399117ef6b43ce397f1844f13e479f41277861b365d8ce3835e7592f9

Transactions (3)

Coinbase7697b3dfe95d79…21c35e8c85b227

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

a433bf86299c44…ba60d0865eb089

1 in → 2 out8.3700 XPM226 B

AMxrvZM2…xV5iE9fn AcKerPva…qeeuPChG

adbafe83c4a415…12ef908b9aea43

1 in → 1 out8.4200 XPM158 B

AekLq4Sw…ueWMfyir

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.

8.405 × 10⁹⁶(97-digit number)

84050682668408978499…38303185342952592639

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

8.405 × 10⁹⁶(97-digit number)

84050682668408978499…38303185342952592639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.405 × 10⁹⁶(97-digit number)

84050682668408978499…38303185342952592641

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

1.681 × 10⁹⁷(98-digit number)

16810136533681795699…76606370685905185279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.681 × 10⁹⁷(98-digit number)

16810136533681795699…76606370685905185281

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

3.362 × 10⁹⁷(98-digit number)

33620273067363591399…53212741371810370559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.362 × 10⁹⁷(98-digit number)

33620273067363591399…53212741371810370561

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

6.724 × 10⁹⁷(98-digit number)

67240546134727182799…06425482743620741119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.724 × 10⁹⁷(98-digit number)

67240546134727182799…06425482743620741121

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

1.344 × 10⁹⁸(99-digit number)

13448109226945436559…12850965487241482239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.344 × 10⁹⁸(99-digit number)

13448109226945436559…12850965487241482241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.689 × 10⁹⁸(99-digit number)

26896218453890873119…25701930974482964479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #937,353

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