Block #922,351

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:05:38 AM · Difficulty 10.9155 · 5,872,986 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

78b584b67d6ae7c4a92b9bd532aa930b73563334e5d47ab3326a7d15322ad376

View on Chainz ↗

Height

#922,351

Difficulty

10.915522

Transactions

Size

115.98 KB

Version

Bits

0aea5fae

Nonce

186,530,969

Timestamp

2/4/2015, 10:05:38 AM

Confirmations

5,872,986

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7186ab732f6bf338a9b50f1c1d6a059bd98a66bd12edb2e307dc603a6ea1c2b8

Transactions (5)

Coinbasefe05d0da2ffeb4…e8d6f0af4a85ed

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

8f0af56a21ae03…b8f77f5a287dfe

200 in → 1 out1296.1564 XPM28.95 KB

AKuP4XsJ…owbodNxQ

f9f6e67fa627e2…2a93c0aa48da0a

200 in → 1 out1065.2389 XPM28.94 KB

AKuP4XsJ…owbodNxQ

5c72905c01a145…b7b2d1971ed2a7

200 in → 1 out967.0248 XPM28.94 KB

AKuP4XsJ…owbodNxQ

cf8fa0fd253e3b…48c333af73a53b

200 in → 1 out839.0965 XPM28.94 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.

5.407 × 10⁹⁹(100-digit number)

54077818780823494519…57382851086406287359

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

5.407 × 10⁹⁹(100-digit number)

54077818780823494519…57382851086406287359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.407 × 10⁹⁹(100-digit number)

54077818780823494519…57382851086406287361

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

1.081 × 10¹⁰⁰(101-digit number)

10815563756164698903…14765702172812574719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.081 × 10¹⁰⁰(101-digit number)

10815563756164698903…14765702172812574721

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

2.163 × 10¹⁰⁰(101-digit number)

21631127512329397807…29531404345625149439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.163 × 10¹⁰⁰(101-digit number)

21631127512329397807…29531404345625149441

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

4.326 × 10¹⁰⁰(101-digit number)

43262255024658795615…59062808691250298879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.326 × 10¹⁰⁰(101-digit number)

43262255024658795615…59062808691250298881

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

8.652 × 10¹⁰⁰(101-digit number)

86524510049317591231…18125617382500597759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.652 × 10¹⁰⁰(101-digit number)

86524510049317591231…18125617382500597761

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