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Block #2,634,417

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 9:29:37 PM Β· Difficulty 11.2436 Β· 4,208,832 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27dd8c81362d61969b9cd51a93e7e5707cc8f907115449ef64f0010a6f9d0574
View on Chainz β†—

Height

#2,634,417

Difficulty

11.243593

Transactions

2

Size

3.31 KB

Version

2

Bits

0b3e5c1c

Nonce

297,270,428

Timestamp

4/28/2018, 9:29:37 PM

Confirmations

4,208,832

Mined by

⛏️ P2SHAGcVy5VnxuuFX4wbUCLv1zHvCaRUpPz3Ym

Merkle Root

f24176e663149a50e181a51569968f728cf140a1273339989553d83a4826c095
Transactions (2)
Coinbase09df9c3fb26445…1c25c33ab2aa05
1 in β†’ 1 out7.9400 XPM110 B
AGcVy5Vn…RUpPz3Ym
ccaab77b9b6d16…0c7c74326af9d6
21 in β†’ 2 out534.5765 XPM3.12 KB
AUhu7AeS…pG78RP7MAPDLbqKj…GS3f3RTS
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.

3.035 Γ— 10⁹⁷(98-digit number)
30357401520894538277…59719259694201456639
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
3.035 Γ— 10⁹⁷(98-digit number)
30357401520894538277…59719259694201456639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.035 Γ— 10⁹⁷(98-digit number)
30357401520894538277…59719259694201456641
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
6.071 Γ— 10⁹⁷(98-digit number)
60714803041789076554…19438519388402913279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.071 Γ— 10⁹⁷(98-digit number)
60714803041789076554…19438519388402913281
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
1.214 Γ— 10⁹⁸(99-digit number)
12142960608357815310…38877038776805826559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.214 Γ— 10⁹⁸(99-digit number)
12142960608357815310…38877038776805826561
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
2.428 Γ— 10⁹⁸(99-digit number)
24285921216715630621…77754077553611653119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.428 Γ— 10⁹⁸(99-digit number)
24285921216715630621…77754077553611653121
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
4.857 Γ— 10⁹⁸(99-digit number)
48571842433431261243…55508155107223306239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.857 Γ— 10⁹⁸(99-digit number)
48571842433431261243…55508155107223306241
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
9.714 Γ— 10⁹⁸(99-digit number)
97143684866862522487…11016310214446612479
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:57,990,368 XPMΒ·at block #6,843,248 Β· updates every 60s
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