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Block #156,112

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2013, 6:11:52 PM Β· Difficulty 9.8676 Β· 6,643,076 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a536a4fee5e12f96b11324474c9ed6a7acc81164dde1e768b216b0487790fd21
View on Chainz β†—

Height

#156,112

Difficulty

9.867561

Transactions

1

Size

200 B

Version

2

Bits

09de187d

Nonce

34,442

Timestamp

9/8/2013, 6:11:52 PM

Confirmations

6,643,076

Mined by

⛏️ P2SHAQE5juVGf2GjfXcDEExb1YTp8cv2LcRcDH

Merkle Root

e9588228940510293de8862dd619b2de8bf44f12c69e42ad17b8a9489eff20cc
Transactions (1)
Coinbasee9588228940510…b8a9489eff20cc
1 in β†’ 1 out10.2500 XPM109 B
AQE5juVG…v2LcRcDH
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.

4.388 Γ— 10⁹⁢(97-digit number)
43888153790904740692…53192659027749774239
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
4.388 Γ— 10⁹⁢(97-digit number)
43888153790904740692…53192659027749774239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.388 Γ— 10⁹⁢(97-digit number)
43888153790904740692…53192659027749774241
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
8.777 Γ— 10⁹⁢(97-digit number)
87776307581809481385…06385318055499548479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.777 Γ— 10⁹⁢(97-digit number)
87776307581809481385…06385318055499548481
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
1.755 Γ— 10⁹⁷(98-digit number)
17555261516361896277…12770636110999096959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.755 Γ— 10⁹⁷(98-digit number)
17555261516361896277…12770636110999096961
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
3.511 Γ— 10⁹⁷(98-digit number)
35110523032723792554…25541272221998193919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.511 Γ— 10⁹⁷(98-digit number)
35110523032723792554…25541272221998193921
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
7.022 Γ— 10⁹⁷(98-digit number)
70221046065447585108…51082544443996387839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,637,542 XPMΒ·at block #6,799,187 Β· updates every 60s
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