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Block #159,068

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2013, 8:49:09 PM Β· Difficulty 9.8655 Β· 6,658,311 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
181104d8eb05cab3f249430ee03f8b6480708f96ab7a6f31e4f954f8c432d756
View on Chainz β†—

Height

#159,068

Difficulty

9.865548

Transactions

1

Size

199 B

Version

2

Bits

09dd9495

Nonce

259,677

Timestamp

9/10/2013, 8:49:09 PM

Confirmations

6,658,311

Mined by

⛏️ P2SHARwEjnekTmEd4gDgSnACXGZ9UNXN12RHSr

Merkle Root

2abc86c3daa9d5dad1c5841a23c1069383f000bf97e54ba1a13f25c03b5597fe
Transactions (1)
Coinbase2abc86c3daa9d5…3f25c03b5597fe
1 in β†’ 1 out10.2600 XPM109 B
ARwEjnek…XN12RHSr
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.

4.632 Γ— 10⁹³(94-digit number)
46320803804372365190…67283786022750234059
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
4.632 Γ— 10⁹³(94-digit number)
46320803804372365190…67283786022750234059
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.632 Γ— 10⁹³(94-digit number)
46320803804372365190…67283786022750234061
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
9.264 Γ— 10⁹³(94-digit number)
92641607608744730381…34567572045500468119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.264 Γ— 10⁹³(94-digit number)
92641607608744730381…34567572045500468121
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
1.852 Γ— 10⁹⁴(95-digit number)
18528321521748946076…69135144091000936239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.852 Γ— 10⁹⁴(95-digit number)
18528321521748946076…69135144091000936241
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
3.705 Γ— 10⁹⁴(95-digit number)
37056643043497892152…38270288182001872479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.705 Γ— 10⁹⁴(95-digit number)
37056643043497892152…38270288182001872481
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
7.411 Γ— 10⁹⁴(95-digit number)
74113286086995784304…76540576364003744959
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:57,783,073 XPMΒ·at block #6,817,378 Β· updates every 60s
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