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Block #37,613

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 10:53:27 AM Β· Difficulty 8.0516 Β· 6,759,198 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2c822e5748393f2ba1ebbd589e27a3b31c855b70cd9373dc348b3457f0ab99a1
View on Chainz β†—

Height

#37,613

Difficulty

8.051609

Transactions

1

Size

201 B

Version

2

Bits

080d3637

Nonce

533

Timestamp

7/14/2013, 10:53:27 AM

Confirmations

6,759,198

Mined by

⛏️ P2SHAMxKwCCcpQHBDXYQ4X8aV63v6UEZ6JsCVT

Merkle Root

d61984c6548812dbd136a4600637095fffe0ef16038256407410f54f8eb520bf
Transactions (1)
Coinbased61984c6548812…10f54f8eb520bf
1 in β†’ 1 out15.4000 XPM110 B
AMxKwCCc…EZ6JsCVT
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.

2.688 Γ— 10⁹⁢(97-digit number)
26881773827925667369…41949567765008069279
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
2.688 Γ— 10⁹⁢(97-digit number)
26881773827925667369…41949567765008069279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.688 Γ— 10⁹⁢(97-digit number)
26881773827925667369…41949567765008069281
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
5.376 Γ— 10⁹⁢(97-digit number)
53763547655851334739…83899135530016138559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.376 Γ— 10⁹⁢(97-digit number)
53763547655851334739…83899135530016138561
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
1.075 Γ— 10⁹⁷(98-digit number)
10752709531170266947…67798271060032277119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.075 Γ— 10⁹⁷(98-digit number)
10752709531170266947…67798271060032277121
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
2.150 Γ— 10⁹⁷(98-digit number)
21505419062340533895…35596542120064554239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.150 Γ— 10⁹⁷(98-digit number)
21505419062340533895…35596542120064554241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,618,503 XPMΒ·at block #6,796,810 Β· updates every 60s
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