Block #922,338

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 9:49:47 AM · Difficulty 10.9156 · 5,888,302 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2bba1d7d006236a8f8800da31d9126d5dc395c4d4cd316f25ffc6471b8be3b31

View on Chainz ↗

Height

#922,338

Difficulty

10.915576

Transactions

Size

115.98 KB

Version

Bits

0aea632a

Nonce

846,954,615

Timestamp

2/4/2015, 9:49:47 AM

Confirmations

5,888,302

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

89eb51f7ff9d89df2ecdc1ebc2d2440c58b41be0518febfe635265f7927a2ce5

Transactions (5)

Coinbasef5c4292851d775…c4029cfb55170c

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

6b9ae41cb5b7a6…994ca0e610a546

200 in → 1 out1019.5960 XPM28.95 KB

AKuP4XsJ…owbodNxQ

927c5c9a950060…58233a7603a3be

200 in → 1 out1051.3899 XPM28.93 KB

AKuP4XsJ…owbodNxQ

8ed9cb6f02b563…e9d756c38e8236

200 in → 1 out951.1181 XPM28.95 KB

AKuP4XsJ…owbodNxQ

939551c65d3188…197c6fc8561d7a

200 in → 1 out1105.7413 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.

2.073 × 10⁹⁵(96-digit number)

20736452995859455522…68768999804268582719

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

2.073 × 10⁹⁵(96-digit number)

20736452995859455522…68768999804268582719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.073 × 10⁹⁵(96-digit number)

20736452995859455522…68768999804268582721

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

4.147 × 10⁹⁵(96-digit number)

41472905991718911045…37537999608537165439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.147 × 10⁹⁵(96-digit number)

41472905991718911045…37537999608537165441

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

8.294 × 10⁹⁵(96-digit number)

82945811983437822091…75075999217074330879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.294 × 10⁹⁵(96-digit number)

82945811983437822091…75075999217074330881

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

1.658 × 10⁹⁶(97-digit number)

16589162396687564418…50151998434148661759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.658 × 10⁹⁶(97-digit number)

16589162396687564418…50151998434148661761

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

3.317 × 10⁹⁶(97-digit number)

33178324793375128836…00303996868297323519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.317 × 10⁹⁶(97-digit number)

33178324793375128836…00303996868297323521

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 #922,338

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