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Block #4,002,510

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/22/2020, 5:02:36 AM Β· Difficulty 10.8398 Β· 2,808,344 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cd86fc4819de73d8d83f3b4dd016ffd7ddf73ee7a402daaff8d299718a5432c9
View on Chainz β†—

Height

#4,002,510

Difficulty

10.839835

Transactions

2

Size

720 B

Version

2

Bits

0ad6ff71

Nonce

1,168,408,280

Timestamp

12/22/2020, 5:02:36 AM

Confirmations

2,808,344

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

0441b7e1742912ebdc3e8d28d3743cc64bd2c0a41bedf0f1ede21ce89710e5da
Transactions (2)
Coinbased1986f10d4bd66…35102d16e86273
1 in β†’ 1 out8.5100 XPM109 B
ASiq2qtK…VMhmk7yL
144333f2026a26…af45f7c2e509a0
3 in β†’ 2 out1.0200 XPM521 B
AcVngSWg…W5HPin9MAS6YGDud…6aEnLt3T
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.

9.882 Γ— 10⁹³(94-digit number)
98824270139998039276…04431203494813014399
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
9.882 Γ— 10⁹³(94-digit number)
98824270139998039276…04431203494813014399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.882 Γ— 10⁹³(94-digit number)
98824270139998039276…04431203494813014401
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
1.976 Γ— 10⁹⁴(95-digit number)
19764854027999607855…08862406989626028799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.976 Γ— 10⁹⁴(95-digit number)
19764854027999607855…08862406989626028801
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
3.952 Γ— 10⁹⁴(95-digit number)
39529708055999215710…17724813979252057599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.952 Γ— 10⁹⁴(95-digit number)
39529708055999215710…17724813979252057601
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
7.905 Γ— 10⁹⁴(95-digit number)
79059416111998431421…35449627958504115199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.905 Γ— 10⁹⁴(95-digit number)
79059416111998431421…35449627958504115201
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
1.581 Γ— 10⁹⁡(96-digit number)
15811883222399686284…70899255917008230399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.581 Γ— 10⁹⁡(96-digit number)
15811883222399686284…70899255917008230401
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:57,730,929 XPMΒ·at block #6,810,853 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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