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Block #156,773

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2013, 4:23:25 AM Β· Difficulty 9.8689 Β· 6,653,540 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
352becd00bc681b79b6705cfc3391fa0b3bc93c58b555149d91106216fe7311e
View on Chainz β†—

Height

#156,773

Difficulty

9.868895

Transactions

1

Size

198 B

Version

2

Bits

09de6fe2

Nonce

199,592

Timestamp

9/9/2013, 4:23:25 AM

Confirmations

6,653,540

Mined by

⛏️ P2SHAQE5juVGf2GjfXcDEExb1YTp8cv2LcRcDH

Merkle Root

22afbe2edc3867c594bce13c42d11f9eb200d43c6029033c69e86d670e297f38
Transactions (1)
Coinbase22afbe2edc3867…e86d670e297f38
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.

2.035 Γ— 10⁹³(94-digit number)
20356447743369187252…70778759036708580219
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
2.035 Γ— 10⁹³(94-digit number)
20356447743369187252…70778759036708580219
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.035 Γ— 10⁹³(94-digit number)
20356447743369187252…70778759036708580221
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
4.071 Γ— 10⁹³(94-digit number)
40712895486738374505…41557518073417160439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.071 Γ— 10⁹³(94-digit number)
40712895486738374505…41557518073417160441
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
8.142 Γ— 10⁹³(94-digit number)
81425790973476749010…83115036146834320879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.142 Γ— 10⁹³(94-digit number)
81425790973476749010…83115036146834320881
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
1.628 Γ— 10⁹⁴(95-digit number)
16285158194695349802…66230072293668641759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.628 Γ— 10⁹⁴(95-digit number)
16285158194695349802…66230072293668641761
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
3.257 Γ— 10⁹⁴(95-digit number)
32570316389390699604…32460144587337283519
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:57,726,581 XPMΒ·at block #6,810,312 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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