Block #561,386

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/25/2014, 12:12:45 PM · Difficulty 10.9650 · 6,234,876 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe025347a8468d401ca668c03a14f20e7d4f8767bedef4e0e5f32d55eca1bef4

View on Chainz ↗

Height

#561,386

Difficulty

10.964979

Transactions

Size

1.23 KB

Version

Bits

0af708de

Nonce

122,925,734

Timestamp

5/25/2014, 12:12:45 PM

Confirmations

6,234,876

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

167e68936bf5124fe8c7c80d3aabb871b382a4d96980b944febdd72c07350df4

Transactions (5)

Coinbasea3700ef81c29cb…022cdb89e4ccc6

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

e39fd98388662b…004e55133378d8

2 in → 2 out10.8724 XPM374 B

AKtZFh49…nYxhFKZQ AY2MMHQo…FPQjgQGx

948efd77fb82ed…f8ed9462baaa99

1 in → 2 out6.7474 XPM226 B

AP6gYnym…DmrMV5Tp AcVexCzF…SY75pd2v

a13eedf1527778…f2894242d70991

1 in → 2 out5.7171 XPM226 B

AG8u7ddV…cU5QJSqk AYqgdr9C…6YVE4RMF

515d1a4f37e65b…e5eb818098e575

1 in → 2 out4.6961 XPM227 B

AS9ZCvju…bu3NEFwZ AXSnx2iv…fGxnQpE6

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.

1.980 × 10⁹⁸(99-digit number)

19802782284494616722…15022203142356625999

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

1.980 × 10⁹⁸(99-digit number)

19802782284494616722…15022203142356625999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.980 × 10⁹⁸(99-digit number)

19802782284494616722…15022203142356626001

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

3.960 × 10⁹⁸(99-digit number)

39605564568989233444…30044406284713251999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.960 × 10⁹⁸(99-digit number)

39605564568989233444…30044406284713252001

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

7.921 × 10⁹⁸(99-digit number)

79211129137978466889…60088812569426503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.921 × 10⁹⁸(99-digit number)

79211129137978466889…60088812569426504001

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

1.584 × 10⁹⁹(100-digit number)

15842225827595693377…20177625138853007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.584 × 10⁹⁹(100-digit number)

15842225827595693377…20177625138853008001

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

3.168 × 10⁹⁹(100-digit number)

31684451655191386755…40355250277706015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.168 × 10⁹⁹(100-digit number)

31684451655191386755…40355250277706016001

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

6.336 × 10⁹⁹(100-digit number)

63368903310382773511…80710500555412031999

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