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Block #187,506

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/30/2013, 2:27:59 PM Β· Difficulty 9.8683 Β· 6,629,352 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e3070fc541dde0b1b41b7cd4317325e9ca9733bc14944bd2e4cc4cf02dc1addb
View on Chainz β†—

Height

#187,506

Difficulty

9.868296

Transactions

1

Size

211 B

Version

2

Bits

09de48a7

Nonce

50,331,825

Timestamp

9/30/2013, 2:27:59 PM

Confirmations

6,629,352

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

d82ce58fdf39ad271678e5f09a6e3e667fadacb594080cc49846b43106559ca3
Transactions (1)
Coinbased82ce58fdf39ad…46b43106559ca3
1 in β†’ 1 out10.2500 XPM116 B
AcLBm5Z9…S683d7c3
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.

6.777 Γ— 10¹⁰⁢(107-digit number)
67777422291678603270…57851478806854420479
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
6.777 Γ— 10¹⁰⁢(107-digit number)
67777422291678603270…57851478806854420479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.777 Γ— 10¹⁰⁢(107-digit number)
67777422291678603270…57851478806854420481
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
1.355 Γ— 10¹⁰⁷(108-digit number)
13555484458335720654…15702957613708840959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.355 Γ— 10¹⁰⁷(108-digit number)
13555484458335720654…15702957613708840961
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
2.711 Γ— 10¹⁰⁷(108-digit number)
27110968916671441308…31405915227417681919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.711 Γ— 10¹⁰⁷(108-digit number)
27110968916671441308…31405915227417681921
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
5.422 Γ— 10¹⁰⁷(108-digit number)
54221937833342882616…62811830454835363839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.422 Γ— 10¹⁰⁷(108-digit number)
54221937833342882616…62811830454835363841
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
1.084 Γ— 10¹⁰⁸(109-digit number)
10844387566668576523…25623660909670727679
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:57,778,907 XPMΒ·at block #6,816,857 Β· updates every 60s
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