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Block #3,498,852

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/3/2020, 6:37:38 PM Β· Difficulty 10.9357 Β· 3,340,688 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
595a1b304fd5b2443c18a5d8feefeb3e07a2ce66743140824150e00941ac5319
View on Chainz β†—

Height

#3,498,852

Difficulty

10.935691

Transactions

2

Size

391 B

Version

2

Bits

0aef896f

Nonce

1,209,166,460

Timestamp

1/3/2020, 6:37:38 PM

Confirmations

3,340,688

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

46ebc44fc7c5585d463c431b3a06c7ad25a5ef1161b2c1053170e52399d67cd1
Transactions (2)
Coinbase7d987efdd104ae…99fd385fa2c5fd
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
3a0260907c3018…f6a31803677f3a
1 in β†’ 1 out9.9900 XPM191 B
AH1VJjsK…14wmz78Y
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.

6.908 Γ— 10⁹³(94-digit number)
69082118840627976692…70676912763179424079
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
6.908 Γ— 10⁹³(94-digit number)
69082118840627976692…70676912763179424079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.908 Γ— 10⁹³(94-digit number)
69082118840627976692…70676912763179424081
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
1.381 Γ— 10⁹⁴(95-digit number)
13816423768125595338…41353825526358848159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.381 Γ— 10⁹⁴(95-digit number)
13816423768125595338…41353825526358848161
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
2.763 Γ— 10⁹⁴(95-digit number)
27632847536251190677…82707651052717696319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.763 Γ— 10⁹⁴(95-digit number)
27632847536251190677…82707651052717696321
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
5.526 Γ— 10⁹⁴(95-digit number)
55265695072502381354…65415302105435392639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.526 Γ— 10⁹⁴(95-digit number)
55265695072502381354…65415302105435392641
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
1.105 Γ— 10⁹⁡(96-digit number)
11053139014500476270…30830604210870785279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.105 Γ— 10⁹⁡(96-digit number)
11053139014500476270…30830604210870785281
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:57,960,611 XPMΒ·at block #6,839,539 Β· updates every 60s
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