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Block #212,952

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/16/2013, 2:50:53 PM Β· Difficulty 9.9198 Β· 6,596,162 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f296b0ec555625bbdacfe72d8e83a822601749cd74d5e8e8bb82c22f20b44664
View on Chainz β†—

Height

#212,952

Difficulty

9.919762

Transactions

1

Size

198 B

Version

2

Bits

09eb758c

Nonce

102,488

Timestamp

10/16/2013, 2:50:53 PM

Confirmations

6,596,162

Mined by

⛏️ P2SHAQVe2UA1iTQ9DYzoq3WAtRFrUDVMZmsiXq

Merkle Root

727c5e3d3becd4458899ca4da2296960398c2ba2c5bc60d6cc7ee63fdab32c42
Transactions (1)
Coinbase727c5e3d3becd4…7ee63fdab32c42
1 in β†’ 1 out10.1500 XPM109 B
AQVe2UA1…VMZmsiXq
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.

1.361 Γ— 10⁹²(93-digit number)
13616482006756810084…47997211161264399979
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
1.361 Γ— 10⁹²(93-digit number)
13616482006756810084…47997211161264399979
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.361 Γ— 10⁹²(93-digit number)
13616482006756810084…47997211161264399981
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
2.723 Γ— 10⁹²(93-digit number)
27232964013513620168…95994422322528799959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.723 Γ— 10⁹²(93-digit number)
27232964013513620168…95994422322528799961
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
5.446 Γ— 10⁹²(93-digit number)
54465928027027240337…91988844645057599919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.446 Γ— 10⁹²(93-digit number)
54465928027027240337…91988844645057599921
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
1.089 Γ— 10⁹³(94-digit number)
10893185605405448067…83977689290115199839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.089 Γ— 10⁹³(94-digit number)
10893185605405448067…83977689290115199841
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
2.178 Γ— 10⁹³(94-digit number)
21786371210810896134…67955378580230399679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,716,969 XPMΒ·at block #6,809,113 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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