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Block #2,657,112

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/11/2018, 4:54:48 PM Β· Difficulty 11.6755 Β· 4,179,405 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9c9ec8e5f1d692c3ea60f36e9ed44ef3995ab8b1b2286cc4e4cc807d37b16e87
View on Chainz β†—

Height

#2,657,112

Difficulty

11.675464

Transactions

2

Size

571 B

Version

2

Bits

0baceb39

Nonce

8,886,316

Timestamp

5/11/2018, 4:54:48 PM

Confirmations

4,179,405

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

70839b372dfd2981e622e84fab67809c399eb58b870d56393ea8bcbb04a8c36c
Transactions (2)
Coinbase28cd3d56a061a6…04ca438620af4b
1 in β†’ 1 out7.3300 XPM109 B
Adqah8zh…1WwoHJ9t
9dd42f7ad37f1d…2cf1831bd39de1
2 in β†’ 2 out200.0688 XPM373 B
APam1QKu…z5xJrsz1AdSmYq5j…mbsGbq72
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.

2.048 Γ— 10⁹³(94-digit number)
20486374310526842463…92262734950594420209
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
2.048 Γ— 10⁹³(94-digit number)
20486374310526842463…92262734950594420209
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.048 Γ— 10⁹³(94-digit number)
20486374310526842463…92262734950594420211
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
4.097 Γ— 10⁹³(94-digit number)
40972748621053684926…84525469901188840419
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.097 Γ— 10⁹³(94-digit number)
40972748621053684926…84525469901188840421
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
8.194 Γ— 10⁹³(94-digit number)
81945497242107369852…69050939802377680839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.194 Γ— 10⁹³(94-digit number)
81945497242107369852…69050939802377680841
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
1.638 Γ— 10⁹⁴(95-digit number)
16389099448421473970…38101879604755361679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.638 Γ— 10⁹⁴(95-digit number)
16389099448421473970…38101879604755361681
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
3.277 Γ— 10⁹⁴(95-digit number)
32778198896842947941…76203759209510723359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.277 Γ— 10⁹⁴(95-digit number)
32778198896842947941…76203759209510723361
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
6.555 Γ— 10⁹⁴(95-digit number)
65556397793685895882…52407518419021446719
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:57,936,413 XPMΒ·at block #6,836,516 Β· updates every 60s
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