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Block #1,974,313

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/8/2017, 8:54:50 AM Β· Difficulty 10.7548 Β· 4,843,153 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
807f83ed4937ab7f24d4fbbf8a01f6c375a87504ce961931ffcec5145b2172d9
View on Chainz β†—

Height

#1,974,313

Difficulty

10.754850

Transactions

2

Size

66.04 KB

Version

2

Bits

0ac13dd5

Nonce

517,826,628

Timestamp

2/8/2017, 8:54:50 AM

Confirmations

4,843,153

Mined by

⛏️ P2SHANuXtdC2UwXP5vNNBaCj7tqJMQnasCK7an

Merkle Root

e687a46bfce6109c08dd818f7e94cb154fa589794c314f6fb3f1ff8b5584bfa7
Transactions (2)
Coinbasec7a31d2d13cd0a…b00651ffcf9eb6
1 in β†’ 1 out9.3100 XPM109 B
ANuXtdC2…nasCK7an
e21ab7c50dd3fc…8f5a5e68ab7676
455 in β†’ 2 out5000.0100 XPM65.84 KB
AHWAAk5Q…nc3GfWe7AZw3qtEj…66F9CiiW
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.

4.569 Γ— 10⁹⁷(98-digit number)
45698351625627071151…50628470214468157439
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
4.569 Γ— 10⁹⁷(98-digit number)
45698351625627071151…50628470214468157439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.569 Γ— 10⁹⁷(98-digit number)
45698351625627071151…50628470214468157441
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
9.139 Γ— 10⁹⁷(98-digit number)
91396703251254142303…01256940428936314879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.139 Γ— 10⁹⁷(98-digit number)
91396703251254142303…01256940428936314881
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
1.827 Γ— 10⁹⁸(99-digit number)
18279340650250828460…02513880857872629759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.827 Γ— 10⁹⁸(99-digit number)
18279340650250828460…02513880857872629761
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
3.655 Γ— 10⁹⁸(99-digit number)
36558681300501656921…05027761715745259519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.655 Γ— 10⁹⁸(99-digit number)
36558681300501656921…05027761715745259521
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
7.311 Γ— 10⁹⁸(99-digit number)
73117362601003313842…10055523431490519039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.311 Γ— 10⁹⁸(99-digit number)
73117362601003313842…10055523431490519041
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:57,783,779 XPMΒ·at block #6,817,465 Β· updates every 60s
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