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Block #661,922

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2014, 8:16:56 AM Β· Difficulty 10.9564 Β· 6,141,381 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
08fbac1171e2fd9c5313023fda567858cbc0bab9d63d21fc2afe9d201c9103b0
View on Chainz β†—

Height

#661,922

Difficulty

10.956375

Transactions

1

Size

207 B

Version

2

Bits

0af4d4fb

Nonce

901,713,237

Timestamp

8/4/2014, 8:16:56 AM

Confirmations

6,141,381

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

12bf1637b0a96a1afdec6d174d0f4cbd38fad4a49238aa1e3a61184f9c584a1a
Transactions (1)
Coinbase12bf1637b0a96a…61184f9c584a1a
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.239 Γ— 10⁹⁷(98-digit number)
22399049931996218956…25183141024956316159
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.239 Γ— 10⁹⁷(98-digit number)
22399049931996218956…25183141024956316159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.239 Γ— 10⁹⁷(98-digit number)
22399049931996218956…25183141024956316161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.479 Γ— 10⁹⁷(98-digit number)
44798099863992437912…50366282049912632319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.479 Γ— 10⁹⁷(98-digit number)
44798099863992437912…50366282049912632321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
8.959 Γ— 10⁹⁷(98-digit number)
89596199727984875824…00732564099825264639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.959 Γ— 10⁹⁷(98-digit number)
89596199727984875824…00732564099825264641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.791 Γ— 10⁹⁸(99-digit number)
17919239945596975164…01465128199650529279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.791 Γ— 10⁹⁸(99-digit number)
17919239945596975164…01465128199650529281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.583 Γ— 10⁹⁸(99-digit number)
35838479891193950329…02930256399301058559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.583 Γ— 10⁹⁸(99-digit number)
35838479891193950329…02930256399301058561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
7.167 Γ— 10⁹⁸(99-digit number)
71676959782387900659…05860512798602117119
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,670,451 XPMΒ·at block #6,803,302 Β· updates every 60s
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