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Block #1,169,847

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2015, 1:53:37 PM Β· Difficulty 10.9357 Β· 5,663,235 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
14065c5852be4707519321e712d9d574cbee64e5c01de6c2cb13b29f65aea6bd
View on Chainz β†—

Height

#1,169,847

Difficulty

10.935682

Transactions

1

Size

200 B

Version

2

Bits

0aef88de

Nonce

1,808,244,471

Timestamp

7/25/2015, 1:53:37 PM

Confirmations

5,663,235

Mined by

⛏️ P2SHAWYim9Co7Jb4KDVAjSVy9XtwrZbitzi8C2

Merkle Root

9b4de336b7aff3c8a7603273d0116a50bc7acc2782f65e71fb769142b0245d48
Transactions (1)
Coinbase9b4de336b7aff3…769142b0245d48
1 in β†’ 1 out8.3500 XPM110 B
AWYim9Co…bitzi8C2
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.

1.592 Γ— 10⁹⁴(95-digit number)
15920890727827527318…32677487752154223839
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
1.592 Γ— 10⁹⁴(95-digit number)
15920890727827527318…32677487752154223839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.592 Γ— 10⁹⁴(95-digit number)
15920890727827527318…32677487752154223841
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
3.184 Γ— 10⁹⁴(95-digit number)
31841781455655054636…65354975504308447679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.184 Γ— 10⁹⁴(95-digit number)
31841781455655054636…65354975504308447681
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
6.368 Γ— 10⁹⁴(95-digit number)
63683562911310109272…30709951008616895359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.368 Γ— 10⁹⁴(95-digit number)
63683562911310109272…30709951008616895361
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
1.273 Γ— 10⁹⁡(96-digit number)
12736712582262021854…61419902017233790719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.273 Γ— 10⁹⁡(96-digit number)
12736712582262021854…61419902017233790721
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
2.547 Γ— 10⁹⁡(96-digit number)
25473425164524043709…22839804034467581439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.547 Γ— 10⁹⁡(96-digit number)
25473425164524043709…22839804034467581441
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:57,908,830 XPMΒ·at block #6,833,081 Β· updates every 60s
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