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Block #139,727

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2013, 4:45:58 AM Β· Difficulty 9.8319 Β· 6,676,202 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bf1fba166e13bae37c913d3c575ba9254d4e310787b2e54fca892fe6a9f5ff6c
View on Chainz β†—

Height

#139,727

Difficulty

9.831888

Transactions

1

Size

198 B

Version

2

Bits

09d4f69e

Nonce

39,081

Timestamp

8/29/2013, 4:45:58 AM

Confirmations

6,676,202

Mined by

⛏️ P2SHAP52EE3FezHothJTJo3Xw2Hi1LZhqfNP3e

Merkle Root

2aec32ee1c51779c16ef2ad7e3d8a2a98a17fbe83efcd92877bc5c0591d21f8a
Transactions (1)
Coinbase2aec32ee1c5177…bc5c0591d21f8a
1 in β†’ 1 out10.3300 XPM109 B
AP52EE3F…ZhqfNP3e
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.

8.409 Γ— 10⁹¹(92-digit number)
84096042884050170585…90494911102699928099
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
8.409 Γ— 10⁹¹(92-digit number)
84096042884050170585…90494911102699928099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.409 Γ— 10⁹¹(92-digit number)
84096042884050170585…90494911102699928101
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
1.681 Γ— 10⁹²(93-digit number)
16819208576810034117…80989822205399856199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.681 Γ— 10⁹²(93-digit number)
16819208576810034117…80989822205399856201
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
3.363 Γ— 10⁹²(93-digit number)
33638417153620068234…61979644410799712399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.363 Γ— 10⁹²(93-digit number)
33638417153620068234…61979644410799712401
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
6.727 Γ— 10⁹²(93-digit number)
67276834307240136468…23959288821599424799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.727 Γ— 10⁹²(93-digit number)
67276834307240136468…23959288821599424801
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
1.345 Γ— 10⁹³(94-digit number)
13455366861448027293…47918577643198849599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.345 Γ— 10⁹³(94-digit number)
13455366861448027293…47918577643198849601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,771,544 XPMΒ·at block #6,815,928 Β· updates every 60s
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