Block #922,370

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:25:44 AM · Difficulty 10.9155 · 5,902,399 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e81e3bc95ad0c3fef6cb03e76a65da403a249d3b5dbed2ba6a874a3cf20da713

View on Chainz ↗

Height

#922,370

Difficulty

10.915510

Transactions

Size

116.00 KB

Version

Bits

0aea5ed7

Nonce

971,338,886

Timestamp

2/4/2015, 10:25:44 AM

Confirmations

5,902,399

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cb4923c6f35726a651db41a1a783364c397018845c3be18093f35dc0331ff285

Transactions (5)

Coinbase6ffc3e5f1cc2de…c12a2f285555cc

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

1ea6ef0cf37a70…44c59d530e1c18

200 in → 1 out1060.3354 XPM28.95 KB

AKuP4XsJ…owbodNxQ

8ee86db917de1e…5beb0214264e11

200 in → 1 out983.2284 XPM28.94 KB

AKuP4XsJ…owbodNxQ

ef93e2e35d5e75…10fd930cb90fc3

200 in → 1 out897.8288 XPM28.95 KB

AKuP4XsJ…owbodNxQ

4832db21f12c4f…d8eba04fd45583

200 in → 1 out1061.2880 XPM28.95 KB

AKuP4XsJ…owbodNxQ

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.

1.102 × 10¹⁰⁰(101-digit number)

11028284051986289644…19981675662517862399

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

1.102 × 10¹⁰⁰(101-digit number)

11028284051986289644…19981675662517862399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.102 × 10¹⁰⁰(101-digit number)

11028284051986289644…19981675662517862401

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

2.205 × 10¹⁰⁰(101-digit number)

22056568103972579289…39963351325035724799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.205 × 10¹⁰⁰(101-digit number)

22056568103972579289…39963351325035724801

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

4.411 × 10¹⁰⁰(101-digit number)

44113136207945158579…79926702650071449599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.411 × 10¹⁰⁰(101-digit number)

44113136207945158579…79926702650071449601

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

8.822 × 10¹⁰⁰(101-digit number)

88226272415890317159…59853405300142899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.822 × 10¹⁰⁰(101-digit number)

88226272415890317159…59853405300142899201

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

1.764 × 10¹⁰¹(102-digit number)

17645254483178063431…19706810600285798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.764 × 10¹⁰¹(102-digit number)

17645254483178063431…19706810600285798401

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

3.529 × 10¹⁰¹(102-digit number)

35290508966356126863…39413621200571596799

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 #922,370

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