Block #1,243,197

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/19/2015, 7:22:44 AM · Difficulty 10.7514 · 5,582,211 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ccaec3f258376b723f1e2b7dcdf2651a8d0cd4ad463be942e6d4bac9f0623b1b

View on Chainz ↗

Height

#1,243,197

Difficulty

10.751371

Transactions

Size

2.15 KB

Version

Bits

0ac059dd

Nonce

1,984,243,198

Timestamp

9/19/2015, 7:22:44 AM

Confirmations

5,582,211

Mined by

⛏️ P2SHAGnwWcaUv2b7cstZWqcLuj83Gd9wqwHJMF

Merkle Root

a56ecc6cdcbbc0ecaa45dec4e2ce2507aff2fa4712efccee784910de73dbac2f

Transactions (4)

Coinbase022234989ca67e…dd36c00e934297

1 in → 1 out8.6800 XPM109 B

AGnwWcaU…9wqwHJMF

e303801ada89f8…ea53754e024114

10 in → 2 out85.5321 XPM1.52 KB

AHuReMPy…i35GpKTA AGhXVDpi…Yo6Z7LzC

21616f1db41742…1879e6304b45a6

1 in → 2 out8.6200 XPM225 B

AeRaNNK1…cPN5BiRF AJQoWLbj…ZnqBStwu

36395b3002e977…bdf139f6adb7a4

1 in → 2 out1.5928 XPM227 B

ATfGqVuL…LGTACqWs APHfVo86…ZaZzhZpD

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.

1.455 × 10⁹⁴(95-digit number)

14552866529263173389…26370873082251372799

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

1.455 × 10⁹⁴(95-digit number)

14552866529263173389…26370873082251372799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.455 × 10⁹⁴(95-digit number)

14552866529263173389…26370873082251372801

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

2.910 × 10⁹⁴(95-digit number)

29105733058526346778…52741746164502745599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.910 × 10⁹⁴(95-digit number)

29105733058526346778…52741746164502745601

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

5.821 × 10⁹⁴(95-digit number)

58211466117052693556…05483492329005491199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.821 × 10⁹⁴(95-digit number)

58211466117052693556…05483492329005491201

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

1.164 × 10⁹⁵(96-digit number)

11642293223410538711…10966984658010982399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.164 × 10⁹⁵(96-digit number)

11642293223410538711…10966984658010982401

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

2.328 × 10⁹⁵(96-digit number)

23284586446821077422…21933969316021964799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.328 × 10⁹⁵(96-digit number)

23284586446821077422…21933969316021964801

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 #1,243,197

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