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Block #667,220

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2014, 12:41:36 PM Β· Difficulty 10.9623 Β· 6,139,369 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3c9b52207aaff50ce5125f8b9e88a4aea97e12e55ec0217f77034a42d9a3799a
View on Chainz β†—

Height

#667,220

Difficulty

10.962283

Transactions

2

Size

547 B

Version

2

Bits

0af65826

Nonce

223,168,478

Timestamp

8/7/2014, 12:41:36 PM

Confirmations

6,139,369

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9650c19a563332576f6b81f7bed1cb964bb2f77119e13a781e3f071cada4bf9a
Transactions (2)
Coinbase158703e22d2ae8…ca6cd4fee1c92b
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
932718682949de…ec768a7dc0ccc6
2 in β†’ 1 out10.0457 XPM339 B
AcsCX7ps…XtYP5nS8
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.

4.943 Γ— 10⁹⁸(99-digit number)
49434045061359927591…62313460751677375359
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
4.943 Γ— 10⁹⁸(99-digit number)
49434045061359927591…62313460751677375359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.943 Γ— 10⁹⁸(99-digit number)
49434045061359927591…62313460751677375361
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
9.886 Γ— 10⁹⁸(99-digit number)
98868090122719855183…24626921503354750719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.886 Γ— 10⁹⁸(99-digit number)
98868090122719855183…24626921503354750721
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
1.977 Γ— 10⁹⁹(100-digit number)
19773618024543971036…49253843006709501439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.977 Γ— 10⁹⁹(100-digit number)
19773618024543971036…49253843006709501441
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
3.954 Γ— 10⁹⁹(100-digit number)
39547236049087942073…98507686013419002879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.954 Γ— 10⁹⁹(100-digit number)
39547236049087942073…98507686013419002881
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
7.909 Γ— 10⁹⁹(100-digit number)
79094472098175884146…97015372026838005759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.909 Γ— 10⁹⁹(100-digit number)
79094472098175884146…97015372026838005761
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
1.581 Γ— 10¹⁰⁰(101-digit number)
15818894419635176829…94030744053676011519
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:57,696,809 XPMΒ·at block #6,806,588 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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