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Block #656,527

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/31/2014, 2:40:31 PM Β· Difficulty 10.9561 Β· 6,139,450 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7218da0daaa5288d074e6fe55b8514bf665f966fffceb5fe05a77db46ad76672
View on Chainz β†—

Height

#656,527

Difficulty

10.956053

Transactions

2

Size

1.00 KB

Version

2

Bits

0af4bfdf

Nonce

85,500,040

Timestamp

7/31/2014, 2:40:31 PM

Confirmations

6,139,450

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e09125b42c29e8658d3e8a2028657c61b04f3378a00aec481d2ebeb10f6575b3
Transactions (2)
Coinbase65d5c519a22a9c…9e9017260b7529
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
7df32b000fc01c…000a871cff0b76
5 in β†’ 2 out41.6100 XPM818 B
ASQ3AWR2…3TjQLS81AX2bVAtJ…GpaxY2ja
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.

1.324 Γ— 10⁹⁹(100-digit number)
13240946273237410630…48375468405100031999
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
1.324 Γ— 10⁹⁹(100-digit number)
13240946273237410630…48375468405100031999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.324 Γ— 10⁹⁹(100-digit number)
13240946273237410630…48375468405100032001
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
2.648 Γ— 10⁹⁹(100-digit number)
26481892546474821260…96750936810200063999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.648 Γ— 10⁹⁹(100-digit number)
26481892546474821260…96750936810200064001
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
5.296 Γ— 10⁹⁹(100-digit number)
52963785092949642520…93501873620400127999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.296 Γ— 10⁹⁹(100-digit number)
52963785092949642520…93501873620400128001
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
1.059 Γ— 10¹⁰⁰(101-digit number)
10592757018589928504…87003747240800255999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.059 Γ— 10¹⁰⁰(101-digit number)
10592757018589928504…87003747240800256001
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
2.118 Γ— 10¹⁰⁰(101-digit number)
21185514037179857008…74007494481600511999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.118 Γ— 10¹⁰⁰(101-digit number)
21185514037179857008…74007494481600512001
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
4.237 Γ— 10¹⁰⁰(101-digit number)
42371028074359714016…48014988963201023999
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:57,611,909 XPMΒ·at block #6,795,976 Β· updates every 60s
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