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Block #2,861,275

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/30/2018, 1:44:29 PM Β· Difficulty 11.6741 Β· 3,982,800 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
280977546b43bcda7926cceaed512964a8557e8cea484d618f302d7ae110bb61
View on Chainz β†—

Height

#2,861,275

Difficulty

11.674143

Transactions

1

Size

200 B

Version

2

Bits

0bac94a2

Nonce

725,196,383

Timestamp

9/30/2018, 1:44:29 PM

Confirmations

3,982,800

Mined by

⛏️ P2SHATC2BD6vFYYWPveV5ZezVCUXQwfu2FddXj

Merkle Root

8100afbf011f7aab3e068fd9642541b468beaf34042b3eab966700ed04ee8a4d
Transactions (1)
Coinbase8100afbf011f7a…6700ed04ee8a4d
1 in β†’ 1 out7.3300 XPM110 B
ATC2BD6v…fu2FddXj
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.

7.054 Γ— 10⁹⁴(95-digit number)
70544464744891752253…82045984771595456719
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
7.054 Γ— 10⁹⁴(95-digit number)
70544464744891752253…82045984771595456719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.054 Γ— 10⁹⁴(95-digit number)
70544464744891752253…82045984771595456721
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
1.410 Γ— 10⁹⁡(96-digit number)
14108892948978350450…64091969543190913439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.410 Γ— 10⁹⁡(96-digit number)
14108892948978350450…64091969543190913441
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
2.821 Γ— 10⁹⁡(96-digit number)
28217785897956700901…28183939086381826879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.821 Γ— 10⁹⁡(96-digit number)
28217785897956700901…28183939086381826881
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
5.643 Γ— 10⁹⁡(96-digit number)
56435571795913401802…56367878172763653759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.643 Γ— 10⁹⁡(96-digit number)
56435571795913401802…56367878172763653761
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
1.128 Γ— 10⁹⁢(97-digit number)
11287114359182680360…12735756345527307519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.128 Γ— 10⁹⁢(97-digit number)
11287114359182680360…12735756345527307521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.257 Γ— 10⁹⁢(97-digit number)
22574228718365360721…25471512691054615039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,996,975 XPMΒ·at block #6,844,074 Β· updates every 60s
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